Basmalah (Bismillahir Rahman Nir Raheem )
Bismillahir Rahman Nir Raheem translates as “In the Name of Allah, the Entirely Merciful and Especially Merciful.”
Allah educated and taught the Prophet Muhammad ﷺto begin the actions with the mention of his most beautiful names i.e Al Asma’ al Husna and commanded him to attribute them to him before every important matter.
He made what he had educated him to do, and what he had taught him, A Sunnah through which all mankind were to confirm., a path along with they were to follow him, and they were to commence their utterances, their letters, their writings, and their requests with it, in such a way that the explicit utterance of the formula “Bismillah” would even suffice to signify what the speaker implicitly intended to do, something which is left unsaid.
Hence it is understood that for instance that, when someone says, Bismillahir Rahman Raheem, and they subsequently starts to recite a surah, that his very following of the formula with the recitation itself imparts the significance of his saying Basmalah, that his intention is “ I recite in the name of Allah , the Most Gracious , the Most Merciful”. Moreover, this is applicable for all the acts for which he recites the Basmalah. 
The Companions started the Book of Allah with Bismillah.
The scholars also agree that Bismillah is a part of an Ayah in Surat An-Naml (Surah no. 27). They disagree over whether it is a separate Ayah before every Surah, or if it is an Ayah, or a part of an Ayah, included in every Surah where the Bismillah appears in its beginning. Ad-Daraqutni also recorded a Hadith from Abu Hurayrah from the Prophet ﷺthat supports this Hadith by Ibn Khuzaymah.
Also, similar statements were attributed to ` Ali Ibn`Abbas and others. The opinion that Bismillah is an Ayah of every Surah, except Al-Bara'ah or At Tauba (Surah no 9), was attributed to (the Companions) Ibn ` Abbas, Ibn ` Umar, Ibn Az-Zubayr, Abu Hurayrah and ` Ali.
On the other hand, Malik, Abu Hanifah and their followers said that Bismillah is not an Ayah in Al-Fatihah or any other Surah. Dawud said that it is a separate Ayah in the beginning of every Surah, not part of the Surah itself, and this opinion was also attributed to Ahmad bin Hanbal.
As for Basmalah aloud during the prayer, those who did not agree that it is a part of Al-Fatihah, state that the Basmalah should not be out loud. The scholars who stated that Bismillah is a part of every Surah (except Surah 9) had different opinions; some of them, such as Ash-Shafi, said that one should recite Bismillah with Al-Fatihah aloud. This is also the opinion of many among the Companions, the Tabi` in and the Imams of Muslims from the Salaf and the later generations.
The proof that these scholars relied on is that, since Bismillah is a part of Al-Fatihah, it should be recited aloud like the rest of Al-Fatihah. Also, An-Nasa'i recorded in his Sunan, Ibn Hibban and Ibn Khuzaymah in their Sahihs and Al-Hakim in the Mustadrak, that Abu Hurayrah once performed the prayer and recited Bismillah aloud. After he finished the prayer, he said, "Among you, I perform the prayer that is the closest to the prayer of the Messenger of Allahﷺ. ''
Ad-Daraqutni, Al-Khat ib and Al-Bayhaqi graded this Hadith Sahih Furthermore, in Sahih Al- Bukhari it is recorded that Anas bin Malik(R) was asked about the recitation of the Prophetﷺ. He said, "His recitation was unhurried. '' He then demonstrated that and recited, while lengthening the recitation of Bismillah Ar-Rahman Ar-Raheem, Also, in the Musnad of Imam Ahmad, the Sunan of Abu Dawud, the Sahih of Ibn Hibban and the Mustadrak of Al-Hakim - it is recorded that Umm Salamah said, "The Messenger of Allah used to distinguish each Ayah during his recitation. Furthermore, Imam Abu
` Abdullah Ash-Shaf i` i and Al-Hakim in his Mustadrak, recorded that Mu` awiyah led the prayer in Al-Madinah and did not recite the Bismillah. The Muhajirin who were present at that prayer criticized that. When Mu`awiyah led the following prayer, he recited the Bismillah aloud. 
Undoubtedly saying the basmalah out loud in al-Faatihah in the prayer is permissible; it is not a bid‘ah (innovation) or haraam. But most of the time in his prayer, the Prophet ﷺdid not pronounce it out loud; rather he recited it quietly.
It was narrated from Anas (R) that the Prophet ﷺ, and Abu Bakr and ‘Umar (R) began the prayer with the words “Al-hamdu Lillahi Rabbi l-‘Aalameen (Praise be to Allah, Lord of the Worlds).”Sahih al-Bukhaari (743)
According to a report narrated by Ahmad (12868), “They did not recite out loud the words ‘Bismillah ir-Rahmaan ir-Raheem (In the name of Allah, the Most Gracious, the Most Merciful).
This is the view of the Hanafis and Hanbalis. The Shaafa‘is differed from them and said that it is Sunnah to recite it out loud, even though the proven Sunnah is not to recite the basmalah out loud. But there is nothing wrong with reciting it out loud, especially if their madhhab is that it is to be recited out loud, so as to soften their hearts.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: … Nevertheless the correct view is that it is not to be recited out loud, although it is prescribed to recite it out loud if that serves a definite interest. Hence it is prescribed for the imam to do that – sometimes – for example, to teach the people who are praying behind him. It is permissible for the worshippers to recite a few words out loud sometimes, and it is also permissible for a man to forego something that is preferable, in order to soften hearts and unite people, lest they be put off from what is in their best interests. For example, the Prophet ﷺdecided not to rebuild the Ka‘bah on the foundations of Ibraheem, because Quraysh had only recently left Jaahiliyyah behind (and were new in Islam), and he was worried that they may be put off by that. He thought that the issue of uniting people and softening their hearts took precedence over the issue of rebuilding the Ka‘bah on the foundations of Ibraheem. Ibn Mas‘ood said, when he offered the prayer in full behind ‘Uthmaan, although he disliked that and objected to him about it, and he was questioned about that: “Dissent is evil.” Hence the imams or leading scholars, such as Ahmad and others, stated that the same applies in the case of the basmalah, and praying Witr as three continuous rak‘ahs, and other issues in which one may turn from that which is preferable to that which is permissible in the interests of softening the hearts or the obligation of teaching them the Sunnah, and so on. Majmoo‘ al-Fataawa (22/436, 437).
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked: What is the ruling on reciting the basmalah out loud?
He replied: The more correct view is that the basmalah should not be recited out loud, and that the Sunnah is to recite it quietly, because it is not part of al-Faatihah. But if it is recited out loud sometimes, there is nothing wrong with that. In fact some of the scholars said that it should be recited out loud sometimes, because it was recited from the Prophet (blessings and peace of Allah be upon him) that he used to recite it out loud. But what is proven from him (blessings and peace of Allah be upon him) is that he did not recite it out loud, and this is the preferred view, that he did not recite it out loud. But if (the imam) recites it out loud in order to soften the hearts of people whose madhhab says that it is to be recited out loud, then I hope that there is nothing wrong with that. Majmoo‘ Fataawa ash-Shaykh Ibn ‘Uthaymeen (13/109)
Basmalah (reciting Bismillah) is recommended before starting any action or deed. For instance, Basmalah is recommended before starting a Khutbah (speech).The Basmalah is also recommended before one enters the place where he wants to relieve himself. Further, Basmalah is recommended at the beginning of ablution. Also, the Basmalah is recommended before eating, for Muslim recorded in his Sahih that the Messenger of Allah ﷺsaid to ` Umar bin Abi Salamah while he was a child under his care, (Say Bismillah, eat with your right hand and eat from whatever is next to you.).
Allah is the Name of the Lord, the Exalted. It is said that Allah is the Greatest Name of Allah, because it is referred to when describing Allah by the various attributes. For instance, Allah said,“(He is Allah, beside Whom La ilaha illa Huwa (none has the right to be worshipped but He) the Knower of the unseen and the seen. He is the Most Gracious, the Most Merciful. He is Allah, beside Whom La ilaha illa Huwa, the King, the Holy, the One free from all defects, the Giver of security, the Watcher over His creatures, the Almighty, the Compeller, the Supreme. Glory be to Allah! (High is He) above all that they associate as partners with Him. He is Allah, the Creator, the Inventor of all things, the Bestower of forms. To Him belong the Best Names. All that is in the heavens and the earth glorify Him. And He is the Almighty, the Wise) Surah Al Hashr 59:22-24
Hence, Allah mentioned several of His Names as Attributes for His Name Allah. Similarly, Allah said “And (all) the Most Beautiful Names belong to Allah, so call on Him by them) Surah Al Araf 7:180.
Also, the Two Sahihs recorded that Abu Hurayrah said that the Messenger of Allahﷺsaid,Allah has ninety-nine Names, one hundred minus one, whoever counts (and preserves them, will enter Paradise.
Ar-Rahman and Ar-Raheem are two names derived from Ar-Rahmah (the mercy), but Rahman has more meanings that pertain to mercy than Ar-Raheem. There is a statement by Ibn Jarir that indicates that there is a consensus on this meaning. Further, Al-Qurtubi said, "The proof that these names are derived (from Ar Rahmah), is what At-Tirmidhi recorded - and graded Sahih from ` Abdur-Rahman bin ` Awf (R) that he heard the Messenger of Allah ﷺsay, Allah the Exalted said, 'I Am Ar-Rahman. I created the Raham (womb, i.e. family relations) and derived a name for it from My Name. Hence, whoever keeps it, I will keep ties to him, and whoever severs it, I will sever ties with him.')
He then said, "This is a text that indicates the derivation.'' He then said, "The Arabs denied the name Ar-Rahman, because of their ignorance about Allah and His attributes.''
Al-Qurtubi said, "It was said that both Ar-Rahman and Ar-Raheem have the same meaning, such as the words Nadman and Nadim, as Abu ` Ubayd has stated. Abu ` Ali Al-Farisi said, ` Ar-Rahman, which is exclusively for Allah, is a name that encompasses every type of mercy that Allah has. Ar-Raheem is what effects the believers, for Allah said,“And He is ever Raheem (merciful) to the believers” Surah Ahzab 33:43.
Also, Ibn `Abbas said - about Ar-Rahman and Ar-Raheem, ` They are two soft names, one of them is softer than the other (meaning it carries more implications of mercy).
`Uthman bin Zufar related that Al-` Azrami said about Ar-Rahman and Ar-Raheem, "He is Ar-Rahman with all creation and Ar-Raheem with the believers.
 Tafsir Ibn Kathir http://www.islamwb.com/tafsir-ibn-kathir-pdf